Question

A nucleus of rest splits into two nuclear parts having radii in the ratio 1 : 2. Their velocities are in the ratio.

Options

• 1 : 8

• 1 : 4

• 4 : 1

• 8 : 1

Answer 1

8 : 1

Explanation:

If A₁ and A₂ are the mass numbers of two parts.

The radius of the nucleus is given by,

`R = R_0(A)^{1"/"3}`

So, `R_1 = R_0(A_1)^{1"/"3}  "and"  R_2 = R_0(A_2)^{1"/"3}`

⇒ `R_1/R_2 = (A_1/A_2)^{1"/"3}`

⇒ `A_1/A_2 = (R_1/R_2)^3 = (1/2)^3 = 1/8`

∴ Ratio of masses, `m_1/m_2 = A_1/A_2 = 1/8`

From the conservation of momentum,

`m_1"v"_1 = m_2"v"_2`

⇒ `"v"_1/"v"_2 = m_2/m_1 = 8/1` or 8 : 1